@article{Mendoza Iturralde_Tkachuk_2002, title={Cofinitely and co-countably projective spaces}, volume={3}, url={https://polipapers.upv.es/index.php/AGT/article/view/2062}, DOI={10.4995/agt.2002.2062}, abstractNote={<p>We show that X is cofinitely projective if and only if it is a finite union of Alexandroff compactatifications of discrete spaces. We also prove that X is co-countably projective if and only if X admits no disjoint infinite family of uncountable cozero sets. It is shown that a paracompact space X is co-countably projective if and only if there exists a finite set B C X such that B C U ϵ τ (X) implies â”‚X\Uâ”‚ ≤ ω. In case of existence of such a B we will say that X is concentrated around B. We prove that there exists a space Y which is co-countably projective while there is no finite set B C Y around which Y is concentrated. We show that any metrizable co-countably projective space is countable. An important corollary is that every co-countably projective topological group is countable.</p>}, number={2}, journal={Applied General Topology}, author={Mendoza Iturralde, Pablo and Tkachuk, Vladimir V.}, year={2002}, month={Oct.}, pages={185–195} }